A fuel system is provided for supplying pressurized fuel, in particular dimethyl ether (DME) or a blend thereof, to an internal combustion engine. The fuel system includes a fuel pump, which has a pumping mechanism arranged partly in a housing containing lube oil, a drain line connected to the housing and suitable for draining at least fuel vapor from an interior of the housing, a lube oil supply line connected to the housing, a lube oil supply valve installed in the lube oil supply line, a seal installed between the pumping mechanism and the housing for preventing at least lube oil leakage to the outside of the housing, and a drain valve installed in the drain line, wherein both the drain valve and lube oil supply valve are controlled to be closed during an engine non-running state for preventing fuel vapor leakage from the housing.